I am trying to typeset a letter x (in both lower- and uppercase) that has a small circle overlaid exactly onto the (perceived) middle of the character. My current best effort is x\llap{$\circ$}, but not only is the resulting circle somewhat bigger than I want, it is visibly not quite centered on the x.

I am using XeLaTeX, if it helps. I have tried looking for unicode combining characters that would do what I want, but the only two candidates I saw (U+208D "COMBINING RING OVERLAY" and U+20DD "COMBINING ENCLOSING CIRCLE") were both very large, and also shared the failure of centering.

Ideally, I would be able to have a simple command that produces this "custom character", because I will need to use it many times.

EDIT: I've decided to use the stackengine-based solution, but all the options look good. Thanks!

EDIT 2: I've switched to the tikz-based solution, because it generalizes much better.